My Lenovo Thinkpad doesn't have enough resolution: will the software run properly?

Minimum requirements are what they say: MINIMUM requirements to run the software.

If the latter is the case, would it run if I buy an external monitor?

If that monitor meets or exceeds the minimum requirements, you will be fine.

For Premiere you need at least 1280x800. That means for the vertical resolution your are 32 pixels short and wont be able to operate specific panels within the program.

I have a question. I'm planning on buying Adobe CC, but my Lenovo Thinkpad doesn't have enough resolution. It only has 1366 x 768; lower than the minimum requirements that Adobe has published. 

Now here is my question: Does the software run properly, whilst some of the borders get cut off, or does it geniuinely NOT run?

I'm planning on buying it if it does run; I can just adjust the size of the software. If the latter is the case, would it run if I buy an external monitor?

I want to mainly run softwares like Photoshop, Illustrator, Dimensions and Premiere Pro.